MATHEMATICS 70.419/70.611, CLASS OUTLINE FOR FALL 2002

WEEK	DATES	ASSIGNMENTS	SECTION/BOOK	TOPICS
1	Sep. 9-13	~	LN 8.1	Introduction to the course. What is coding theory. Basics of finite fields. Linear codes.
2	Sep. 16-20	~	LN 8.1	Decoding linear codes. Bounds.
3	Sep. 23-27	A1 out: Sep. 23	LN 8.2; MS 3.1; MS 3.3	2-error-correcting BCH codes. Finite fields. Polynomials.
4	Sep. 30 - Oct. 4	~	LN 1.2-1.4	Review: rings, fields and ideals. Extension fields. Splitting fields.
5	Oct. 7-11	A1 in / A2 out: Oct. 7	LN 2.1; McE 5	Characterization of finite fields. Subfield criterion. Primitive elements and Gauss algorithm.
6	Oct. 14-18	No lecture on Oct. 14	LN 2.3; LN 2.5	Traces, norms and bases. Representation of elements in a finite field.
7	Oct. 21-25	~	LN 3.2; vzGG 14.9	Number of irreducible polynomials. Finding irreducible polynomials. Ben-Or's algorithm.
8	Oct. 28 - Nov. 1	A2 in / A3 out: Oct. 28	vzGG 14.1-14.6	Squarefree, distinct-degree and equal-degree factorization.
9	Nov. 4-8	~	MS 7; vzGG 14.10	Cyclic codes. Minimal polynomials.
10	Nov. 11-15	A3 in / A4 out: Nov. 11	MS 7	BCH codes revisited. Computing minimal polynomials.
11	Nov. 18-22	~	MS 10; HHLLPRW 6	Reed-Solomon codes.
12	Nov. 25-29	~	HHLLPRW 8	Linear feedback shift registers. Convolutional codes.
13	Dec. 2	A4 in: Dec. 2	~	Review of course. Comments on final exam.

vzGG is ``Modern Computer Algebra'', by J. von zur Gathen and J. Gerhard, Cambridge University Press, 1999.
HHLLPRW is ``Coding Theory and Cryptography: the Essentials'', by D.R. Hankerson, D.G Hoffman, D.A. Leonard, C.C. Lindner, K.T. Phelps, C.A. Rodger and J.R. Wall, Marcel Dekker Inc., 2000.
LN is ``Introduction to Finite Fields and Their Applications'', by R. Lidl and H. Niederreiter, Cambridge University Press, 1994.
MS is ``The Theory od Error-Correcting Codes'', by F.J. MacWilliams and N.J.A. Sloane, North-Holland, Elsevier Science, 1977.
McE is ``Finite Fields for Computer Scientists and Engineers'', by R. McEliece, Kluwer Academic Press, 1987.